Fascist is maybe not a good term, because fascism is actually quite specific and to some extent euro-centric (plus, nowadays it just means "bad people" without people necessarily understanding what fascism actually is).
But China seems to be a country run on a totalitarian and ethnic nationalist ideology.
Only if words don't mean things, though you can see how the least charitable (which is not to say least accurate; who knows) reading of Chinese policy would lead you there. In particular, I think there's a trap where if you cherry pick from Maoist China and modern China, you can assembly a Frankenchina that meets some of the definitions.
There are some pretty obvious elements of most common academic definitions of fascism that China flunks, no matter how you read them; for instance, Chinese society has not been mass-mobilized and militarized by any reasonable definition of those terms. Modern China not only doesn't reject modernism, it wholeheartedly embraces it. If there's a secular civic religion, with ceremony and liturgy, it isn't powerful enough to crowd out other faiths; there is a national patriotic spirit, but it isn't articulated through quasi-mystical symbols and rituals. Violence isn't employed for its own cathartic sake, and is largely "professionalized".
People want to use fascism as a shorthand for "authoritarian nationalism", but it isn't; there are plenty of examples of authoritarian nationalist states that are demonstrably not fascist --- in fact, there are plenty of right-wing authoritarian nationalist states that aren't.
Maybe a good acid test for this: if you were living in a fascist state, you'd know it, in much the same you'd know if you were living in an actual according-to-Hoyle theocracy. China is a huge country and millions of people there live with a relationship between themselves and the state that we would recognize in the west.
I want also to acknowledge that it is kind of squicky to debate whether China is "fascist", in that it's an extremely loaded term that carries implications for ordinary Chinese people living their lives (that's part of the point of fascism). But a discussion about what fascism is or isn't is at least more in the spirit of HN than a lot of the other comments on these threads.
If you want to get technical it's a very advanced fascist dictatorship - the way it leverages elements of capitalism, for example. An innovative fascist dictatorship, even. But ideologically speaking, it's very simple.
Maybe the community could help me to understand whether this is accurate?